Motivated by the newly observed narrow structures Omega _b(6316)^-, Omega _b(6330)^-, Omega _b(6340)^-, and Omega _b(6350)^- in the Xi _b^0 K^- mass spectrum, we investigate the strong decays of the low-lying Omega _b states within the ^3P_0 model systematically. According to their masses and decay widths, the observed Omega _b(6316)^-, Omega _b(6330)^-, Omega _b(6340)^-, and Omega _b(6350)^- resonances can be reasonably assigned as the lambda -mode Omega _b(1P) states with J^P=1/2^-, 3/2^-, 3/2^-, and 5/2^-. Meanwhile, the remaining P-wave state with J^P=1/2^- should have a rather broad width, which can hardly be observed by experiments. For the Omega _b(2S) and Omega _b(1D) states, our predictions show that these states have relatively narrow total widths and mainly decay into the Xi _b {bar{K}}, Xi _b^prime {bar{K}} and Xi _b^{prime *} {bar{K}} final states. These abundant theoretical predictions may be valuable for searching more excited Omega _b states in future experiments.